RADICALS COMMON MISTAKES

Transcription

1 RADICALS COMMON MISTAKES 1 10/0/009

2 Radicals-Notatio, Defiitio, ad Simplifyig How to Uderstad the Defiitio ad Notatio Notatio: a root, radical, a radicad. Square root,, but the two is NOT writte (i.e. 16 ) Cube root,, (i.e. 8 ). Defiitio ad Simplifyig: a requires a to be factored ito repeatig factors ad for repeatig factors, oe factor ca be pulled through the radical: Examples: requires the factor to repeat twice requirig the factor to repeat three times 8 Not correctly factorig ito simplified form. Icorrect: Correct: /0/009

3 Radicals-Negative Radicals How to Evaluate Negative Radicals a Sice (where is a positive iteger,) implies oly the positive roots, there are times whe the radicad, a, ca be egative. If the radicad, a, is egative, the it is defied oly if is a positive ODD iteger. Tryig to evaluate egative radicads whe is eve. Cofusig ad. Forgettig the egative sig whe evaluatig radicals with POSITIVE ODD ROOTS. Example: Simply 8. Solutio: Sice is a positive odd iteger, a-8 is permissible. So, 8. 10/0/009

4 Radicals-Multiplicatio/Divisio How to Multiply/Divide Radicals Multiplicatio a b Divisio Solutio: a a 8 b ab b Note: must be the same ad a ad b must be defied such that yields a Real solutio. Not combiig or separatig radical expressios whe simplifyig expressios. Example 1: Simplify: Example : Simplify:. Solutio: /0/009

5 Radicals-Additio/Subtractio How to Add/Subtract Radicals Note: Radicals ca oly be added/subtracted together if they have the ad same root with the same radicad. Sometimes, radicals must be simplified before they ca be combied. Not reducig radicals to their SIMPLIFIED form before tryig to add or subtract the radicals. Example 1: Simplify. Solutio: First, , which the substitutes to become /0/009

6 Radicals- Ratioalizig How to Ratioalize Radicals A radical is cosidered to be i proper form if there is o radical i the deomiator( the bottom umber i a fractio). To put a radical expressio i proper form is called ratioalizig. It ivolves multiplyig the expressio by a clever form of 1. It is the radical i the deomiator that will idicate what that form will be. Choosig the icorrect clever form of 1. Simplify 4. Icorrect: Correct: /0/009

7 Radicals- Cojugatig Radical Expressios How to Cojugate Radical Expressio Give, the cojugate is a b or visa versa. Cojugates are multiplied together which cacels out the radical because ( x + y)(x y) x y shows that the middle terms fall out. a + b Usig the wrog cojugate. Icorrectly multiplyig the terms together. Simplify by ratioalizig the deomiator: 4 +. Icorrect: Cojugate is Correct: Cojugate is 4 So 4 10/0/ (4 ) ( )

8 Radicals- Solvig Radical Equatios How to Solve Radical Equatios Whe solvig equatios ivolvig radicals, the first idea is to isolate the radical oto oly oe side of the equatio before attemptig to solve the equatio. The, raise both sides to the power that is the reciprocal of the root. Now, the variable is to the first power ad is i simplified form. Not oticig the value of the root problem, resultig i solvig for the wrog power. Not repeatig the process of solvig util the variable is to the first power. Example: Solve x 6 for x. Solutio: x 9 x 9 ( x) 9 x /0/009